We introduce a new approach for robotic manipulation tasks in human settings that necessitates understanding the 3D geometric connections between a pair of objects. Conventional end-to-end training approaches, which convert pixel observations directly into robot actions, often fail to effectively understand complex pose rela- tionships and do not easily adapt to new object configurations. To overcome these issues, our method focuses on learning the 3D geometric relationships, particularly how critical parts of one object relate to those of another. We employ Weighted SVD in our standalone model to analyze pose relationships both in articulated parts and in free-floating objects. For instance, our model can comprehend the spatial relationship between an oven door and the oven body, as well as between a lasagna plate and the oven. By concentrating on the 3D geometric connections, our strategy empowers robots to carry out intricate manipulation tasks based on object-centric perspectives

翻译：摘要：我们提出了一种新方法，用于在人类环境中执行机器人操作任务，该方法需理解物体对之间的三维几何关联。传统端到端训练方法将像素观测直接转化为机器人动作，往往难以有效理解复杂的位姿关系，且不易适应新的物体配置。为解决这些问题，我们的方法专注于学习三维几何关系，特别是某一物体的关键部件与另一物体关键部件之间的关联。我们在独立模型中采用加权奇异值分解（Weighted SVD）来分析铰接部件和自由浮动物体的位姿关系。例如，模型可理解烤箱门与烤箱箱体之间的空间关系，以及千层面烤盘与烤箱之间的空间关系。通过聚焦三维几何连接，该策略使机器人能够基于物体中心视角执行复杂操作任务。